Group #14569747 — subgroups

Subgroups — #14569747

Order 2432.

612 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597390	C₂	1	2	yes	maximal, complemented
2	C₂×#10597393	C₂	1	2	yes	maximal
3	C₂×#10597321	C₂	1	1	yes	maximal, characteristic
4	#11926479	C₂	1	8	yes	maximal, complemented
5	#11926390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
8	C₂²×D₇₆	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₁₉×C₄⋊Q₈	—	2	4	no	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	#10597393	—	2	8	no	—
14	#10597390	—	2	8	no	—
15	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
16	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	8	yes	—
17	C₂×Dic₁₉⋊C₄	C₂²	1	8	yes	—
18	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
19	#10597321	—	2	4	no	—
20	C₁₉⋊#95	C₂²	1	4	yes	—
21	C₂³×D₁₉	C₂³	1	2	yes	—
22	C₂×Q₈×C₁₉	—	2	4	no	—
23	C₂×Q₈×C₁₉	—	2	4	no	—
24	C₂×Q₈×C₁₉	—	2	4	no	—
25	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×Dic₁₉	C₂³	1	2	yes	—
29	C₂²×Dic₁₉	C₂³	1	4	yes	—
30	C₂×D₇₆	—	2	4	no	—
31	C₂×D₇₆	—	2	2	no	—
32	C₂×Dic₃₈	—	2	4	no	—
33	C₂×Dic₃₈	—	2	2	no	—
34	C₄⋊C₄×C₁₉	—	2	8	no	—
35	C₄²×C₁₉	D₄	1	4	yes	—
36	(C₂×D₁₉)⋊C₄	—	2	8	no	—
37	(C₂×D₁₉)⋊C₄	—	2	16	no	—
38	Dic₁₉⋊C₄	—	2	16	no	—
39	C₄×Dic₁₉	D₄	1	8	yes	—
40	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
41	C₂²×D₁₉	—	2	4	no	—
42	C₂²×D₁₉	—	2	2	no	—
43	C₂²×D₁₉	—	2	8	no	—
44	Q₈×C₁₉	—	4	8	no	—
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	2	4	no	—
47	C₂×C₄×C₁₉	—	2	4	no	—
48	C₂×C₄×C₁₉	—	2	4	no	—
49	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
50	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
51	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
52	C₂×Dic₁₉	—	2	8	no	—
53	C₂×Dic₁₉	—	2	4	no	—
54	C₂×Dic₁₉	—	2	2	no	—
55	C₂×Dic₁₉	C₂×D₄	1	8	yes	—
56	D₇₆	—	4	4	no	—
57	Dic₃₈	—	4	4	no	—
58	#2658	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
60	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
61	C₂²×C₁₉	2₋¹⁺⁴	1	4	yes	—
62	C₂×D₁₉	—	4	2	no	—
63	C₂×D₁₉	—	4	4	no	—
64	C₂×D₁₉	—	4	8	no	—
65	C₄×C₁₉	—	2	4	no	—
66	C₄×C₁₉	—	4	4	no	—
67	C₄×C₁₉	#127	1	4	yes	—
68	Dic₁₉	—	2	8	no	—
69	Dic₁₉	—	4	2	no	—
70	C₂×C₄⋊Q₈	—	19	2	no	—
71	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic, complemented
72	C₂×#124	—	19	2	no	—
73	C₂×#124	—	19	1	no	—
74	#399	—	19	8	no	—
75	#376	—	19	1	no	—
76	C₂×C₁₉	C₂×#127	1	1	yes	characteristic
77	C₂×C₁₉	#536	1	2	yes	—
78	C₂×C₁₉	#536	1	4	yes	—
79	D₁₉	—	8	2	no	—
80	C₂²×Q₈	—	19	1	no	—
81	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
82	C₂²×D₄	—	19	1	no	—
83	C₄⋊Q₈	—	2	4	no	—
84	C₄⋊Q₈	—	38	8	no	—
85	#124	—	38	8	no	—
86	#124	—	38	4	no	—
87	C₂×C₄⋊C₄	—	19	8	no	—
88	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
89	C₂×C₂²⋊C₄	—	19	8	no	—
90	C₂×C₂²⋊C₄	—	19	4	no	—
91	C₂×C₄²	—	19	2	no	—
92	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
93	#95	—	19	4	no	—
94	C₁₉	#2658	1	1	yes	characteristic, complemented, Sylow
95	C₂⁴	—	19	2	no	—
96	C₂×Q₈	—	2	4	no	—
97	C₂×Q₈	—	2	4	no	—
98	C₂×Q₈	—	2	4	no	—
99	C₂×Q₈	—	38	4	no	—
100	C₂×Q₈	—	38	2	no	—
101	C₂×D₄	—	38	4	no	—
102	C₂×D₄	—	38	2	no	—
103	C₂²×C₄	—	19	4	no	—
104	C₂²×C₄	—	19	2	no	—
105	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
106	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
107	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
108	C₄⋊C₄	—	2	8	no	—
109	C₄⋊C₄	—	38	16	no	—
110	C₂²⋊C₄	—	38	16	no	—
111	C₂²⋊C₄	—	38	8	no	—
112	C₄²	—	19	8	no	—
113	C₄²	C₂²⋊D₁₉	1	4	yes	—
114	C₂³	—	38	4	no	—
115	C₂³	—	38	8	no	—
116	C₂³	—	38	2	no	—
117	C₂³	C₂³×D₁₉	1	1	yes	characteristic
118	Q₈	—	4	8	no	—
119	Q₈	—	76	4	no	—
120	D₄	—	76	4	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	19	8	no	—
126	C₂×C₄	—	38	8	no	—
127	C₂×C₄	—	38	4	no	—
128	C₂×C₄	—	38	2	no	—
129	C₂×C₄	D₄×D₁₉	1	4	yes	—
130	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
131	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
132	C₂²	—	76	2	no	—
133	C₂²	—	76	4	no	—
134	C₂²	—	76	8	no	—
135	C₂²	C₂×D₄×D₁₉	1	2	yes	—
136	C₂²	#10597433	1	4	yes	—
137	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
138	C₄	—	2	4	no	—
139	C₄	—	4	4	no	—
140	C₄	—	38	8	no	—
141	C₄	—	76	2	no	—
142	C₄	#10597386	1	4	yes	—
143	C₂	—	152	2	no	—
144	C₂	C₂×#10597386	1	1	yes	characteristic
145	C₂	#11927118	1	2	yes	—
146	C₂	#11927119	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597390

C₂

yes

maximal, complemented

C₂×#10597393

C₂

yes

maximal

C₂×#10597321

C₂

yes

maximal, characteristic

#11926479

C₂

yes

maximal, complemented

#11926390

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597393

—

#10597390

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597321

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

D₇₆

—

Dic₃₈

—

#2658

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#127

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×C₄⋊Q₈

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂×C₁₉

C₂×#127

yes

characteristic

C₂×C₁₉

#536

yes

—

C₂×C₁₉

#536

yes

—

D₁₉

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₂²×D₄

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#124

—

#124

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

—

C₁₉

#2658

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

C₂²×D₁₉

yes

—

106

C₂²×C₄

C₂²×D₁₉

yes

—

107

C₂²×C₄

C₂²×D₁₉

yes

characteristic

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₂²⋊C₄

—

111

C₂²⋊C₄

—

112

C₄²

—

113

C₄²

C₂²⋊D₁₉

yes

—

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

C₂³×D₁₉

yes

characteristic

118

Q₈

—

119

Q₈

—

120

D₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

D₄×D₁₉

yes

—

130

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

131

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

C₂×D₄×D₁₉

yes

—

136

C₂²

#10597433

yes

—

137

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

#10597386

yes

—

143

C₂

—

152

—

144

C₂

C₂×#10597386

yes

characteristic

145

C₂

#11927118

yes

—

146

C₂

#11927119

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
prime radical	C₂²×D₇₆	C₂²
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#2658
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

prime radical

C₂²×D₇₆

C₂²

hypercenter

C₂×C₄⋊Q₈

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
1. C₂×#10597390	C₂	semidirect
4. #11926479	C₂	semidirect
5. #11926390	C₂	semidirect
6. C₂×C₁₉×C₄⋊Q₈	C₂	semidirect
71. C₂×C₄⋊Q₈	D₁₉	semidirect
94. C₁₉	#2658	semidirect

H ≅ G/N

type

1. C₂×#10597390

C₂

semidirect

4. #11926479

C₂

semidirect

5. #11926390

C₂

semidirect

6. C₂×C₁₉×C₄⋊Q₈

C₂

semidirect

71. C₂×C₄⋊Q₈

D₁₉

semidirect

94. C₁₉

#2658

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#10597390	2
C₂×#10597393	2
C₂×#10597321	2
#11926479	2
#11926390	2
C₂×C₁₉×C₄⋊Q₈	2
#2658	19

subgroup

index

C₂×C₁₉×C₄⋊Q₈

Subgroups — #14569747

Conjugacy classes of subgroups

Complements

Maximal subgroups